Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem Summary: 0 Modifications of the Oettli-Prager Theorem with Application to the Eigenvalue Problem G. Alefeld, V. Kreinovich, G. Mayer Dedicated to Prof. Dr. Jiirgen Herzberger on the occasion 0/ his 60th birthday. 1 Introduction In this paper we consider the eigenpair set Ep := { (x,).) I Ax = ).x, x i=0, A E [AL A with property P}, (1) where [A] is a given real n x n interval matrix (cf. Alefeld and Herzberger (1983), e.g., for interval analysis) and P is some fixed property such as symmetry, Toeplitz form, etc.. Before we study this set in greater detail we mention other ones which are related to it: When dealing with systems of linear equations Ax - b- , A E Jl{.nxn, bE Jl{.n (2) (Jl{.n Xn set of real n x n matrices, ßRn set of real vectors with n components) there sometimes occurs the problem of varying the input data A, b within certain tolerances and looking for the set S of the resulting solutions x*. Examples of this problem are Wilkinson's backward analysis when solving linear systems on a computer (Wilkinson 1963) and an input-output model in economics which is regulated by (2) with input parameters A, band output x (Maier 1985). In the first example one solves (2) on a computer (assuming A to be nonsingular). Collections: Mathematics